4 papers
Bailey pairs and quantum -series identites. I. The classical identities
Jehanne Dousse, Jeremy Lovejoy
We use Bailey pairs to prove -series identities at roots of unity due to Cohen and Bryson-Ono-Pitman-Rhoades. The proofs use Bailey pairs with quadratic forms developed in the s…
Bailey Pairs and an Identity of Chern-Li-Stanton-Xue-Yee
Shashank Kanade, Jeremy Lovejoy
We show how Bailey pairs can be used to give a simple proof of an identity of Chern, Li, Stanton, Xue, and Yee. The same method yields a number of related identities as well as fal…
Bailey pairs, radial limits of -hypergeometric false theta functions, and a conjecture of Hikami
Jeremy Lovejoy, Rishabh Sarma
In the first part of this paper we prove a conjecture of Hikami on the values of the radial limits of a family of -hypergeometric false theta functions. Hikami conjectured that…
Rank deviations for overpartitions
Jeremy Lovejoy, Robert Osburn
We prove general fomulas for the deviations of two overpartition ranks from the average. These formulas are in terms of Appell--Lerch series and sums of quotients of theta function…